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The concept of transferring forces in a reciprocal way has always been related to the use of timber beams, that is, elongated elements. However, planar components can also be considered; circular tiles, squares, triangles and more articulated or irregular geometrical shapes are all valid alternatives. This report proposes an initial exploration of reciprocal systems based on planar elements in order to guide further morphological studies. It also presents some prototypes, which were developed by the students of the Ecole des Ponts in Paris during two design workshops run in 2012 and 2013.

The construction of concrete shells has always been a difficult and expensive procedure. Preparation of complex formworks, as well as placement of curved reinforcing rods require experience and increase the overall cost. Building concrete shells is even more of concern within the Australian context, where the use of simple and rapid technologies has always been a priority. In the Sixties, Italian architect Dante Bini developed and patented a form-finding and construction technique that aimed to solve this issue, the so-called “Binishells”. This paper investigates Dante Bini’s system, from its conception within the Italian environment until the international success which was reached in the USA and Australia.

In book: "Shell Structures for Architecture - Form finding and optimization", (pp.290-294). Chapter: Appendix C. Publisher: Routledge. Editors: Sigrid Adriaenssens, Philippe Block, Diederik Veenendaal, Chris Williams.

Genetic algorithms are a subclass of evolutionary algorithms. A genetic algorithm (GA) is defined by Goldberg as a “search algorithm based on the mechanics of natural selection and natural genetics”, but another definition, more focused on its way of functioning, is provided by John R. Koza in his 1992 book, “Genetic programming: On the Programming of Computers by Means of Natural Selection”: “The GA is a highly parallel mathematical algorithm that transforms a set (population) of individual mathematical objects [...], each with an associated fitness value, into a new population (i.e. the next generation) using operations patterned after the Darwinian principle of reproduction and survival of the fittest and after naturally occurring genetic operations (notably sexual recombination)”. In other words, in a random population of potential solutions, the best individuals are favoured and combined in order to create better individuals at the nextgeneration.

In book: "Shell Structures for Architecture - Form finding and optimization", (pp.224-236). Chapter: 18. Publisher: Routledge. Editors: Sigrid Adriaenssens, Philippe Block, Diederik Veenendaal, Chris Williams.

Since the introduction of digital technologies, computational design and optimization has been gradually replacing practice based on physical models. Even if born as a set of mere solution strategies, architectural and structural design optimization seems also to be effective in supporting conceptual design. This aspect is highlighted through two design exercises of computational morphogenesis using genetic algorithm (GA). Two key aspects emerge from such processes: the possibility of freely formulating objective functions apart from structural performances, and the opportunity for designers to actively interact throughout the computational process.

Reciprocity is a structural principle that has fascinated designers and builders throughout the world since ancient times. Despite the topic's having been studied by various academics, designers and researchers, a critical overview of the references is still missing, as is an outline and discussion of the current and future promising research/design issues. Further, no single text provides an exhaustive definition of the principle of structural reciprocity and it must be critically reconstructed from several different sources. This paper aims to fill in these gaps, providing a complete and annotated list of references, in which historical examples, as well as patents, research articles and terminological issues are discussed. A consistent definition of structural reciprocity is also proposed, and the promising developments of such a principle are outlined in order to guide designers and researchers in the future.

The concept of transferring forces in a reciprocal way has always been related to the use of elongated timber elements. However, planar components can also be considered - circular tiles, squares, triangles and more articulated or irregular geometries are all valid alternatives. This paper proposes an initial study on reciprocal systems based on planar elements in order to guide further morphological research activities. It also presents some prototypes developed by the students of the École des Ponts in Paris during two workshops run in March 2012 and 2013.

This paper discusses the application of a Multi-Objective Search method to the design of shell structures. Contrasting objectives of lightweight and high stiffness are considered for two case studies with different geometry and constraints. The Multi-Objective search is performed in the frame of the Pareto theory of non-domination, implemented in the NSGA-II algorithm. The research focuses on the way a designer can interact with the search computational procedure, driving it towards the desired solution. Diversely from pure optimization techniques, search strategies as Multi-Objective search produce sets of feasible solutions, which the designer can evaluate and use it their work, accordingly with other architectural requirements and purposes.

This paper deals with a multi-objective design/optimization grid-shell problem. Structural behavior and light absorption/shading have been selected as fitness functions. Such performance criteria can separately lead to different and divergent optimal solutions but, if they are considered as a whole, they are expected to result in several equivalent or similar sub-optimal shapes. This multi-objective optimization problem has been performed here with the aid of a Genetic Algorithm (GA). GAs explore and search widely for suitable solutions and, in this way, they become design tools rather than solution ones. Three benchmarks were established and then a more complex application was made to an existing case study, i.e. the Esplanade in Singapore, designed by DP Architects (DPA) and Michael Wilford & Partners (MWP).

This paper deals with the design of reciprocal spatial configurations, based on the use of planar elements, which are investigated and classified according to their morphological characteristics and design potential. Reciprocal structures were first originated as assemblies of elongated elements. In Europe, the concept of spanning longer distances than the length of the available timber beams was the key reason for the use of such structures, which were therefore called ‘short-beams’. In the East and especially in China, the use of interwoven strips of bamboo for the construction of baskets is an old tradition that was transferred to larger scale objects, and which has also led to the development of reciprocal configurations based on linear elements. In this framework, a study of reciprocal systems, based on the use of 2D planar panels, is proposed. A first morphological classification of reciprocal systems based on planar elements, which have been divided according to the shape of the elements and growth possibilities of their assembly, is provided. Moreover, some research issues for future investigations are highlighted. The presented systems and prototypes were developed by students at the École des Ponts in Paris during their Master’s degree and a workshop run by the authors in March 2012.